Postfix smtp server works from localhost but not from afar

http://serverfault.com –
I'm trying to set up a smtp server on my domain (wixencafe.net), and i'm using postfix for that.
First thing is, postfix delivers emails coming from outside, that is, if i send an email from gmail.com to wixencafe.net, i get the email in my Mailbox/
Second thing is, if i send an email from wixencafe.net (from the server cli via mutt -f Maildir/) to gmail.com, i get it too, so i guess that means everything works fine.
Now, my problem is, if I try to send emails from my desktop (which is not on the same network than my server), it just doesn't work. From thunderbird, i get a delivery error, a
(HowTos)

I have had no luck recently with postfix (see here ). So, I am now looking for a simple SMTP program that will automatically send emails after certain events. This should be a program that can be called from another program when a certain event is detected (I used to use mailx with postfix).